But I’m on a tight budget
Admittedly "tight budget" means different things to different people.... but if a $500*+ RTX 3070 is doable, a quality PSU to run it should be too.
* Remember $500 is the MSRP. Only select models will be available at the pricepoint - and those models will likely be availably (however briefly) at launch. The second wave of cards will probably be supply of the next 'tier' of models, probably in the $550-$600 range, then once supply normalizes, the ~$500 models should be available again.
So unless you get super lucky at launch, you're likely looking at a couple of months before you can even get your hands on a ~$500 3070. More than enough time for most people to pick up a quality PSU .... Again, looking ~$100 for something good, and the Leadex III is the best 'value' at the moment that I'm aware of.
I am on a tight buget so should I just wait tell i get a better power supply?
Also what would happen if my power supply is not compatible?
I would advocate the PSU first. Given the likely timeline to get your hands on a 3070 (going to be more in demand than a 3080 or 3090 - although supply should be greater), you probably have a month or two to handle the PSU first.
As for what 'would' happen if the PSU isn't up to the test (I'm not saying 'not compatible') really depends.
The SMART units aren't great, but they do have some modicum of protections built in, so you're not looking at fire hazard (in all likelihood). What you might experience would be instability, random shutdowns or outright no display when you turn it on.
^^ That would be even when the PSU is new. Add a few weeks/months/years of use (to now, or post-3070) and the problem compounds. It might 'work' initially, but equally it might not. Or it might work for a while. Highly, highly doubtful that PSU would go on forever with a 3070 in it.
Remember, nobody has a problem with a component until they do.
That PSU should be fine for quite a while with a 1050TI, RX570 or 1060 etc (75-150W GPUs), but even then, I wouldn't recommend the unit specifically. Add another 100+W to the equation, and it's a different ballgame.